Consider the Simpsons rule for the integral Z 1 0 f(x) dx, with the given data set:

(a). Compute the numerical integration using Simpsons rule with h = 0.25.

(b) If the error tolerance is 106 , how many points must one use for Simpsons rule with uniform grid?

2. Simpson's rule Consider the Simpson's rule for the integral f() dx with the given data set f(0.00 0.060.240.51 0.84 The plots of the derivatives of f are given below: 1st derivative 2nd derivative 3rd derivative 4th derivative 0.0 1.8 1.6 1.0 1.2 1.0 0.8 0.6 0.4 0.2 2.0 2.5 3.0 3.5 2.0 -2.5 -3.0 -3.5 4.0 0.5 0.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 0.8 1.0 0.0 0.2 0.4 0.6 08 1.0 0.0 0.2 0.4 0.6 0.8 1.0 (a). Compute the numerical integration using Simpson's rule with h 0.25 (b) If the error tolerance is 10-6, how many points must one use for Simpson's rule with uniform grid